Fluid Network Studio

Reynolds number calculator

Reynolds number: mean flow through a pipe of internal diameter DA pipe carrying a mean flow, with the bore diameter D, and a strip showing whether the computed Reynolds number is laminar, transitional or turbulent.Qv = 1.50 m/sDRe = v D / nulaminartrans.turbulent
Re = v D / nu = 74,734 - turbulent

Result

Reynolds number
74,734
Flow regime
Turbulent

See the Reynolds number and flow regime for every pipe in a full network in the Studio.

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The Reynolds number is the dimensionless ratio of inertial to viscous forces in a flow. It is the single best predictor of whether pipe flow is laminar, transitional or turbulent, and it sets the friction factor and the heat-transfer correlations that follow. This calculator returns the Reynolds number and the regime for flow in a circular pipe.

Method

For flow in a circular pipe,

Re = rho v D / mu = v D / nu

where rho is density (kg/m^3), v is mean velocity (m/s), D is internal diameter (m), mu is dynamic viscosity (Pa s) and nu = mu / rho is kinematic viscosity (m^2/s). If you have the volumetric flow rather than the velocity, v = 4Q / (pi D^2), so Re = 4Q / (pi D nu).

Conventional regime boundaries for pipe flow:

  • Laminar: Re < 2300
  • Transitional: 2300 < Re < 4000
  • Turbulent: Re > 4000

These thresholds are conventional, not sharp; transition depends on inlet conditions and disturbances. Citation: Reynolds, O. (1883); see White, Fluid Mechanics.

Limits. The internal pipe diameter is the length scale here. For a non-circular duct the hydraulic diameter is used instead; that is not yet offered in this tool.

Inputs

  • Fluid preset (density and viscosity) or manual density and viscosity.
  • Internal diameter D (mm).
  • Velocity v (m/s) or volumetric flow Q (L/s).

Outputs

  • Reynolds number.
  • Flow regime (laminar, transitional or turbulent).

Worked example

Water at 20 degrees C (kinematic viscosity 1.004 x 10^-6 m^2/s) in a 50 mm pipe at 1.5 m/s:

Re = 1.5 x 0.05 / 1.004e-6 = 74,700

which is well into the turbulent range.

Frequently asked questions

What is the transition value?

Around 2300 for pipe flow is the usual figure for the onset of transition, but it is not a hard line; carefully controlled flows can stay laminar higher.

Which diameter do I use?

The internal diameter of a round pipe. For rectangular or annular ducts you would use the hydraulic diameter, which this single-pipe tool does not yet cover.

Related

New to the terms? See the glossary and how it works, or browse all calculators.